Which of the following numbers is a multiple of 13? ${46,56,72,91,96}$
Explanation: The multiples of $13$ are $13$ $26$ $39$ $52$ ..... In general, any number that leaves no remainder when divided by $13$ is considered a multiple of $13$ We can start by dividing each of our answer choices by $13$ $46 \div 13 = 3\text{ R }7$ $56 \div 13 = 4\text{ R }4$ $72 \div 13 = 5\text{ R }7$ $91 \div 13 = 7$ $96 \div 13 = 7\text{ R }5$ The only answer choice that leaves no remainder after the division is $91$ $ 7$ $13$ $91$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $91$ $91 = 7\times13 13 = 13$ Therefore the only multiple of $13$ out of our choices is $91$. We can say that $91$ is divisible by $13$.